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# Linear & nonlinear functions: missing value

## Video transcript

find the missing value to make the table represent a linear equation so let's see this table right over here so when X is equal to 1 Y is three-halves when X is 2 y is equal to 3 so let's see what happens when X increased by 1 so when X increased by 1 what did Y do well it looks like Y increased by 3 and 1/2 is the same thing as 1 and 1/2 so to go from 1 and 1/2 to 3 it increased by 1 and 1/2 or you could say it increased by 3 halves you could say that 3 is the same thing as 6 halves 6 halves minus 3 halves is another 3 halves all right now when we go from 2 to 3 we're increasing by 1 again in the in X and what are we doing in Y so we're going from 3 which is the same thing as 6 halves to 9 halves so once again we are increasing by 3 halves so in order for this to be a linear equation or a linear relationship every time we increase by 1 in the X direction we need to increase by 3 halves if we increase by 2 we need to increase by 2 times 3 halves so what are we doing over here on this fourth term on the table well we're increasing we're going from 3 to 8 so we are increasing by 5 so we're if we're increasing X by 5 then we need to increase Y we increase Y by 5 times 3 halves or 15 over 2 that's the amount that we have to increase we have to increase Y by if we started at 9 halves and we're going to increase by 15 halves so it's going to be 9 halves plus 15 halves this is how much we increment by remember we increment 3 halves every time X moves 1 this time X moved 5 so we're incrementing by 15 halves or you could say we're incrementing by 3 halves 5 times but this is going to be equal to 9 plus 15 is 24 over 2 which is equal to 12 and so in the box we could write 12 and we are done